Montreal-born Conrad Black says he will keep fighting for his freedom after the U.S. Supreme Court on Tuesday rejected the former media mogul's challenge of his two remaining convictions on fraud and obstruction of justice.

"That court almost never takes a case back and so its decision was expected," Black said in an email to The Canadian Press. "Nor is it a tryer of fact, so its decision today does not imply any agreement with the circuit court's resurrection of two counts, only that it didn't chin itself on our constitutional argument."

The Supreme Court in Washington, D.C., did not comment on the order.

The top court decided last June to significantly limit how U.S. courts apply "honest services" law, which had been used by prosecutors in a number of high-profile cases involving allegations of white-collar crime by corporate executives.

The Supreme Court didn't overturn the convictions but sent the cases back to lower Appeals Courts to determine whether the convictions would hold up if the new standard had been applied correctly.

Black, who had been serving a 6½-year sentence in a U.S. federal prison, has been free since last summer while the appeals run their course.

Set to return to court

Two of Black's three fraud convictions were overturned in October by a U.S. Appeals Court. It upheld one fraud conviction and one for obstruction of justice.

Black is set to return to a Chicago courtroom on June 24 for resentencing on his two remaining fraud convictions.

The U.S. attorney believes Black's original sentence of 6½ years should be reimposed. Though Black has behaved well in prison and helped teach fellow inmates, he has refused to accept responsibility for his crimes, prosecutors said in a court filing ahead of the June sentencing hearing.

Black was freed on bail from a Florida prison last year while he appealed his conviction for defrauding investors. He had served 29 months of a 78-month sentence for the original four convictions.

Black's empire once included the Chicago Sun-Times, the Daily Telegraph of London, and smaller papers across the U.S. and Canada.

With files from The Associated Press